Factoring a Sum of Cubes

I was looking at factoring the sum and difference of two cubes and was wondering if you have any input as to how to teach it for true understanding.

I have not taught this topic much, if at all, in Algebra 1, as it strikes me as rather technical, and better suited to older students.

My hunch is that one way to make this interesting is to present it as a puzzle to students who are familiar with “the box”, aka the generic rectangle, aka the multiplication table format. So here’s an off-the-cuff worksheet: